Knowledge: By the end of the course, the student is expected to
be able to explain the concepts of: a first order language; of
a model of a first order language; of formal deduction; of a
computable relation and function; arithmetization of first
order syntax; the axioms of Zermelo-Fraenkel set theory;
ordinals and cardinals.

Skills: By the end of the course, the student must be able to
define the satisfacation relation, account for the axioms of
the deductive system, define the notion of recursive function,
and prove that a repository of common functions and relations
are recursive, including the coding of basic syntactical
notions. The student must be able to prove the key theorems of
the course, such as the deduction theorem, the
soundness theorem, and the compactness theorem.

Competences: Use of first order languages and structures in
mathematics, the formalization of proofs, the coding of
syntactical notions in arithmetic. Use ordinal analysis and
transfinite recursion.